Abstract
In this paper we introduce a distribution which is an extension of the power Maxwell distribution. This new distribution is constructed based on the quotient of two independent random variables, the distributions of which are the power Maxwell distribution and a function of the uniform distribution (0,1) respectively. Thus the result is a distribution with greater kurtosis than the power Maxwell. We study the general density of this distribution, and some properties, moments, asymmetry and kurtosis coefficients. Maximum likelihood and moments estimators are studied. We also develop the expectation–maximization algorithm to make a simulation study and present two applications to real data.
Highlights
A distribution related to the normal distribution is the slash distribution
The power Maxwell (PM) is a special case of the slash power Maxwell (SPM) model
We studied the mode; moments; statistic order; and asymmetry and kurtosis
Summary
A distribution related to the normal distribution is the slash distribution. Its stochastic representation is the quotient between two independent random variables: a normal distribution and a function of the uniform distribution. Coraddu et al [17] discussed the physics of nuclear reactions in stellar plasma by checking with special emphasis on the importance of the velocity distribution of ions They claimed that the properties (density and temperature) of the weak-coupled solar plasma were analyzed, showing that the ion velocities should deviate from the Maxwell distribution and could be better described by a "weakly-non-extensive Tsallis" distribution. The main object of this paper is to introduce an extension of the PM distribution using slash methodology This new distribution presents a greater kurtosis than the PM distribution, so we can use it to model atypical data.
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